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A279719 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 189", based on the 5-celled von Neumann neighborhood. 4
1, 1, 2, 3, 20, 7, 104, 79, 16, 927, 288, 3135, 2880, 1663, 27776, 22783, 13568, 223743, 250368, 427007, 848896, 1779711, 3622912, 6950911, 14929920, 22323199, 17113088, 184041471, 18300928, 986349567, 363102208, 3410034687, 2520580096, 795475967 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
MATHEMATICA
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 189; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 2], {i , 1, stages - 1}]
CROSSREFS
Sequence in context: A108884 A119584 A344546 * A279672 A364648 A089181
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 17 2016
STATUS
approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)